Fractional-Order Systems Optimal Control via Actor-Critic Reinforcement Learning and Its Validation for Chaotic MFET - Li, Dongdong; Dong, Jiuxiang (IEEE transactions on automation science and engineering, 2025)
Since the existence of fractional order dynamics, it is difficult to obtain an optimality equation to solve for fractional-order optimal control. In this paper, a fractional Hamilton-Jacobi-Bellman (HJB) equation based on error derivative is proposed, and a corresponding online learning algorithm is designed. The scheme can handle the optimal tracking problem for the 0< α ≤ 1 order nonlinear systems. Since the traditional quadratic cost function is unbounded at infinite time and the optimal control derived from the discounted cost function fails to stabilize the system asymptotically, a cost function based on the error derivative is proposed, which can avoid these problems, and the system is not restricted to be zero equilibrium. Then, the fractional HJB equation is derived by constructing an auxiliary signal without directly using the chain rule of differentiation. The optimality, stability and convergence of its solution are proved, and actor-critic neural networks (NNs) are established to perform the RL algorithm. Finally, the algorithm is applied to a chaotic magnetic-field electromechanical transducer (MFET) system to verify the effectiveness and advantages. Note to Practitioners-In engineering, fractional-order dynamics properties are used in many practical systems such as chaotic MFET systems, chaotic arch micro-electro-mechanical systems and fractional order resonant controllers, etc. For these fractional-order systems, traditional integer-order control methods cannot be applied. Moreover, optimal performance with minimal cost/resources can be achieved through optimal control. Therefore, a intelligent control method based on reinforcement learning is proposed in this paper to realize the optimal control for fractional-order systems. The proposed method is applicable to most fractional-order systems and can achieve stable control while optimizing the objective performance and reducing energy consumption. Finally, the proposed algorithm is successfully applied to the chaotic MFET systems.